Interferometric method for improving the resolution of a lithographic system

Abstract

According to one exemplary embodiment of the present invention, a method for writing an arbitrary, two-dimensional pattern using interferometric lithography and classical techniques includes the steps of: (1) creating a pixel array defined by a number of pixels having specific coordinates; (2) mapping pixel information based on the desired pattern, the pixel information including a list of which pixels are activated to define the desired two-dimensional pattern; (3) controlling a relative strength of each pixel for indicating a feature height of a portion of the desired two-dimensional pattern; and (4) controlling a degree that one pixel is shifted in an x-direction and a y-direction relative to original coordinates of the pixel in order to define the desired two-dimensional pattern pixel by pixel.

1. A method for writing an arbitrary, two-dimensional pattern using interferometric lithography comprising the steps of:
 creating a pixel array defined by a number of pixels having specific coordinates; 
 mapping pixel information based on the desired pattern, the pixel information including a list of which pixels are activated to define the desired two-dimensional pattern; 
 controlling a relative strength of each pixel for indicating a feature height of a portion of the desired two-dimensional pattern; 
 controlling a degree that one pixel is shifted in an x-direction and a y-direction relative to original coordinates of the pixel in order to define the desired two-dimensional pattern pixel by pixel; and 
 writing the two-dimensional pattern pixel by pixel on a recording material; wherein each pixel has an associated A coefficient value, an α coefficient value and a β coefficient value, the A coefficient value representing the relative intensity of the pixel, the α coefficient value representing the degree that the pixel is shifted horizontally (x-direction) relative to base coordinates of the pixel, the β coefficient value representing the degree that the pixel is shifted vertically (y-direction) relative to the base coordinates of the pixel, wherein the shifting of one or more pixels forms non-linear features of the pattern. 
 
     
     
       2. The method of  claim 1 , wherein a resulting electric field for a given pixel is determined by the equation:
     E   i,j   =A   i,j   {e   iδ     i,j     [e   ikx   +e   −ikx   e   iφ     i,j     ]+[e   iky   +e   −iky   e   iθ     i,j   ]} 
 
       where δ i,j =[θ i,j −φ i,j ]/2 with φ i,j =2π(i+α i,j )/M and θ i,j =2π(j+β i,j )/M; and wherein the value of the A coefficient is from 0 to 1. 
     
     
       3. The method of  claim 2 , wherein the total deposition on the recording material is given by a two-dimensional sum over the pixel array and is defined as: 
       
         
           
             
               
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       4. A method for writing an arbitrary, two-dimensional pattern using interferometric lithography comprising the steps of:
 creating a pixel array defined by a number of pixels having specific coordinates; 
 mapping pixel information based on the desired pattern, the pixel information including a list of which pixels are activated to define the desired two-dimensional pattern; 
 controlling a relative strength of each pixel for indicating a feature height of a portion of the desired two-dimensional pattern; 
 controlling a degree that one pixel is shifted in an x-direction and a y-direction relative to original coordinates of the pixel in order to define the desired two-dimensional pattern pixel by pixel; and 
 writing the two-dimensional pattern pixel by pixel on a recording material outputting a first beam of light; 
 splitting the first beam into the second and third beams by a first beam splitter, 
 disposing a second beam splitter in the path of the second beam to split it into an x-beam  1  and an x-beam  2 ; 
 disposing a third beam splitter in the path of the third beam to split it into a y-beam  1  and a y-beam  2 ; 
 disposing a first spatial light modulator (SLM) in the path of the x-beam  1 ; 
 disposing a second SLM in the path of the x-beam  2 ; 
 disposing a third SLM in the path of the y-beam  2  and disposing a fourth SLM in the path of the y-beam  1 ; and 
 arranging a plurality of optical components and positioning them relative to the x-beam  1 , the x-beam  2 , the y-beam  1  and the y-beam  2  so that the y-beam  1  and the y-beam  2  interfere in a vertical manner and the x-beam  1  and the x-beam  2  interfere in a horizontal manner and each of the four beams reaches the recording material at the same point and same time; 
 wherein each pixel has an associated A coefficient value, an α coefficient value and a β coefficient, the A coefficient value representing the relative intensity of the pixel, the α coefficient value representing the degree that the pixel is shifted horizontally (x-direction) relative to base coordinates of the pixel, the β coefficient value representing the degree that the pixel is shifted vertically (y-direction) relative to the base coordinates of the pixel, wherein the shifting of one or more pixels forms non-linear features of the pattern; and 
 wherein the SLMs have associated phase factors for controlling the amplitude and phase shifts of the respective beams to cause the four beams to reach the recording material at the same point and same time. 
 
     
     
       5. A system for writing an arbitrary, two-dimensional pattern using interferometric lithography on a recording material comprising:
 a source of a light beam having a prescribed wavelength; 
 a computer having non-transitory tangible media that is configured to create a pixel array defined by a number of pixels having specific base coordinates and permits the two-dimensional pattern to be mapped on the pixel array, wherein each pixel has a corresponding A coefficient, an α coefficient value and β coefficient value, the A coefficient value representing the relative intensity of the pixel, the α coefficient value representing the degree that the pixel is shifted horizontally (x-direction) relative to base coordinates of the pixel, the β coefficient value representing the degree that the pixel is shifted vertically (y-direction) relative to the base coordinates of the pixel, wherein the shifting of one or more pixels forms one or more non-linear features of the pattern, wherein based on inputted information regarding the desired two-dimensional pattern, the computer determines the corresponding A coefficient value, the α coefficient value and the β coefficient value needed for each pixel to form the two-dimensional pattern pixel by pixel; and 
 a device that communicates with the computer and writes the two-dimensional pattern on the recording material using classical interferometric lithography techniques that act on the light beam. 
 
     
     
       6. A method for writing an arbitrary, two-dimensional pattern on a recording material using interferometric lithography and classical techniques comprising the steps of:
 creating a pixel array defined by a number of main pixels having specific coordinates; 
 dividing each main pixel into an M×M subarray of pixels to permit a specific region within one main pixel to be identified by subarray coordinates to permit finer patterns to be established with precise detail on the recording material, where M≦N, where M is a level of resolution enhancement and N is the order of absorption of an N photon absorber which comprises the recording material; 
 generating and treating a light beam classically as a composite electromagnetic wave, the light beam being divided into first and second light beams that carry horizontal (x) information and third and fourth light beams that carry vertical (y) information; and 
 interfering the first and second beams in a horizontal manner on the recording material and interfering the third and fourth beams in a vertical manner on the recording material such that each of the four beams reaches the recording material at the same point same time to write the two-dimensional pattern pixel by pixel; 
 wherein each subarray pixel has an associated A coefficient value, an α coefficient value and a β coefficient value, the A coefficient value representing the relative intensity of the pixel, the α coefficient value representing the degree that the pixel is shifted horizontally (x-direction) relative to base coordinates of the pixel, the β coefficient value representing the degree that the pixel is shifted vertically (y-direction) relative to the base coordinates of the pixel, wherein the shifting of one or more pixels forms non-linear features of the pattern.